Article pubs.acs.org/JPCB
Volume Fraction of Ether Is a Significant Factor in Controlling Conductivity in Proton Conducting Polyether Based Polymer Sol−Gel Electrolytes Benjamin Yancey, Jonathan Jones, and Jason E. Ritchie* Department of Chemistry and Biochemistry, The University of Mississippi, 222 Coulter Hall, University, Mississippi 38677, United States S Supporting Information *
ABSTRACT: We have synthesized several copolymers of methyl polyethylene glycol siloxane (MePEG7SiO3)m and methyl polypropylene glycol siloxane (MePPGnSiO3)m as hydrogen ion (H+) conducting polymer electrolytes. These copolymers were prepared by a sol−gel polymerization of mixtures of the MePEG and MePPG monomers. We synthesized these H+ conducting polymer electrolytes in order to study the relationship between observed ionic conductivity and structural properties such as viscosity, fractional free volume, and volume fraction of ether. We found that viscosity increased as the fraction of the smaller comonomer increased. For the MePPG2/MePPG3 copolymer, an increase in fractional free volume increased the fluidity. The heterogeneous copolymers (PEG/PPG copolymers) obeyed the Doolittle equation, while the homogeneous (PEG/PEG and PPG/PPG) copolymers did not. The increase of FFV did not, however, correspond to an increase in conductivity, as would have been predicted by the Forsythe equation. The conductivity data did correspond to a modified Forsythe equation substituting Volume Fraction of Ether (Vf,ether) for FFV. We conclude that the proton conductivity of MePEG copolymers is more dependent on the volume fraction of ether than on the fractional free volume.
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INTRODUCTION Proton exchange membrane fuel cells (PEMFCs) use a polymer electrolyte to both physically separate the anode from the cathode and conduct hydrogen ions (H+) between the electrodes. Polymer electrolytes have the advantage of being easy to chemically modify, and have properties that support ion mobility as well as mechanical durability.1−3 Currently, Nafion, a sulfonated perfluorinated polymer, is the most widely used proton conducting polymer electrolyte. Nafion has the necessary chemical stability, mechanical properties, and ionic conductivity when hydrated for use in a PEM fuel cell. The major disadvantages of Nafion are its cost, poor hydrophobicity, and hydration dependent conductivity. Alternatively, membranes based on polybenzimidazole (PBI) and phosphoric acid have also been developed with an eye toward higher temperatures without the same water management requirements of Nafion. The hydration dependent ionic conductivity in Nafion limits the operational temperature to below 80 °C.4 The platinum catalytic anode in a PEMFC has a low resistance to CO poisoning (which is commonly present in H2 fuel streams produced from reforming of fossil fuels). These disadvantages necessitate the development of new anhydrous polymer electrolytes for PEM fuel cells, for which the U.S. Department of Energy has set an operational goal of 0.1 S/cm conductivity at 120 °C and 50% relative humidity. Polyethylene glycol (PEG) and poly(ethylene oxide) (PEO), and the related polymer polypropylene glycol (PPG), conduct © 2014 American Chemical Society
small cations in the absence of water. Neither PEG nor PPG have the mechanical stability required to serve as a fuel cell membrane. However, attachment of PEG or PPG groups to an inorganic matrix can form a hybrid organic/inorganic material combining the mechanical properties of the inorganic portion with the anhydrous conductivity of PEG and PPG.5−12 Siloxanes are easy to functionalize, and are chemically and mechanically stable, due to their chemical similarities to silica.13−15 Both PEG and PPG can be coupled to siloxanes by hydrosilylation reactions to form the inorganic/organic hybrid.5,16−22 Siloxane polymers are easily made from the acid catalyzed, sol−gel condensation of chlorosilanes or alkoxysilanes. Polymers formed by this condensation can exhibit the advantages of both the organic and inorganic portions, making them useful as polymer electrolytes. We are interested in how the structure of the polymer electrolyte affects the ionic conductivity. In terms of studying the structure, we look to intrinsic properties of the polymer including viscosity, ionic conductivity, fractional free volume, and volume fraction of the ionically conductive ether component (i.e., either the PEG or PPG units). Free volume theory is used to statistically evaluate glassy or amorphous polymer systems.23 The free volume (vf) is defined as the virtual volume of the molecule (the total volume Received: July 18, 2014 Revised: October 14, 2014 Published: October 14, 2014 13002
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indirectly occupied through random molecular motions, vm) minus the hard sphere volume (van der Waals volume, vw) of the molecule.23−25 Free volume is a scalar quantity that is dependent on the sample size of the material but can be expressed as the sample size independent: molar free volume (Vf, eq 1). When calculating the free volume of a polymer, the molar volume (Vm, eq 2) is first calculated using the density and molecular weight of the molecule, and then, the molar van der Waals volume (Vw) is calculated using the group contribution method developed by Bondi.24,26,27 Further, the fractional free volume (FFV, eq 3) is very useful in describing transport behavior in these systems, and is expressed as the ratio of molar free volume (Vf) to total molar volume (Vm). Fractional free volume is independent of sample geometry and volume and is useful for comparing the free volume of different materials.24,26,27 Vf = Vm − Vw
(1)
MW Vm = d
(2)
(V − Vw ) V FFV = f = m Vm Vm
(3)
Fractional Walden’s Rule: Ληα = constant
Doolittle developed an empirical equation (eq 7) to describe the relationship between free volume and viscosity.29,33 Doolittle’s relationship demonstrates that a smaller fractional free volume results in a smaller fluidity. In eq 7, A and q are material specific constants where A represents the fluidity extrapolated to zero free volume and q is a measure of the liquid’s intermolecular forces. In addition, Vm and Vf are the total molar volume and molar free volume, respectively. The ratio Vm/Vf is equivalent to the inverse fractional free volume (FFV−1), and substitution results in eq 7a. Doolittle’s Equation:
⎡ V ⎤ 1 = A exp⎢ −q m ⎥ η ⎣ Vf ⎦ ⎡ −q ⎤ 1 = A exp⎢ ⎣ FFV ⎥⎦ η
Dphys
F2 [z+2D+C+ + z −2D−C −] RT
⎡ γ ⎤ D = A exp⎢ − ⎣ FFV ⎥⎦
(8)
Forsythe Equation:
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⎛ ACF 2Z2 ⎞ ⎡ −γ ⎤ σ=⎜ ⎟ exp⎢ ⎣ FFV ⎥⎦ ⎝ RT ⎠
(9)
EXPERIMENTAL SECTION Materials. Polyethylene glycol monomethyl ether (CH3(OCH2CH2)nOH = MePEGnOH, Mn = 350, n = 7.24; Aldrich) and polypropylene glycol monomethyl ether (CH3(OCH(CH3)−CH2)nOH = MePPGnOH, Mn = 148.2, 206.3, n = 2, 3; Aldrich) were dried at 60 °C under a vacuum for approximately 24 h prior to use. This paper will refer to poly(ethylene glycol) monomethyl ether Mn = 350 as MePEG7OH, tri(propylene glycol) monomethyl ether Mn = 206.3 as MePPG3OH, and di(propylene glycol) monomethyl ether Mn = 148.2 as MePPG2OH. Copolymers of MePEG7 and MePPG3 will be referred to as MePEG7/MePPG3, MePEG7 and MePPG2 copolymers as MePEG7/MePPG2, and MePPG3 and MePPG2 copolymers as MePPG3/MePPG2. Triethoxysilane (Aldrich), allyl bromide (Acros), Karstedt’s catalyst (platinum(0)-1,3-divinyl-1,1,3,3-tetramethyldisiloxane complex solution in xylene, Pt ∼2%; Aldrich), and sodium sulfite (Fisher) were all used as received. Amberlite IRA400(Cl) anion exchange resin (Aldrich) and Amberlite IR-
(4)
(5)
Walden’s rule (eq 6a) defines the relationship between fluidity and conductivity. In this equation, Λ is the molar equivalent conductivity and η is the viscosity. This rule generally holds true for ideal solutions in which there are no ion−ion interactions. However, in real electrolyte solutions, the fractional Walden rule (eq 6b) is a better descriptor of real physical observations.31,32 In eq 6b, α is a constant between 0 and 1, with α = 1 representing ideal behavior (eq 6a); that is, viscosity is the only force impeding ionic mobility. Where 0 < α < 1, other forces are present that impede ionic mobility. Walden’s Rule: Λη = constant
(7a)
Cohen−Turnbull Equation:
Nernst−Einstein Equation: σION =
(7)
Cohen and Turnbull combined the Stokes−Einstein equation (eq 4) with the Doolittle equation (eq 7), resulting in the Cohen−Turnbull equation (eq 8). In this equation, A incorporates all of the constants in eq 4 and γ is the same as q in the Doolittle equation.25 The Cohen−Turnbull equation illustrates that, as the fractional free volume increases, the diffusion coefficient will also increase. Forsythe combined the Nernst−Einstein equation (eq 5) with the Cohen−Turnbull equation (eq 8), resulting in the Forsythe equation (eq 9).34 The Forsythe equation shows that, when the fractional free volume is increased, the ionic conductivity (σ) should increase as well.
In free volume theory, the transport properties of a material (e.g., viscosity - η, conductivity - σ, and diffusion coefficient D) are dependent on the free volume.28,29 For example, diffusion through a material is described as translation through openings in the free volume in a particle’s vicinity.25 Free volume, in this description, is a measure of the concentration of void space in a material. The Stokes−Einstein equation (eq 4) predicts that an increase in fluidity (fluidity = η−1) will result in an increase in the diffusion coefficient (D). The Nernst−Einstein equation (eq 5) predicts that an increase in the diffusion coefficient of either ion results in a proportional increase in the ionic conductivity.30 Equations 4 and 5 together indicate that an increase in the fluidity will cause an increase in the ionic conductivity. Stokes−Einstein Equation:
kT = 6πηRH
(6b)
(6a) 13003
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120H cation exchange resin (Aldrich) were used as received. Phosphorus tribromide (99%; Aldrich) was prepared as a 1.98 M solution in dry diethyl ether using 55.91 g of phosphorus tribromide dissolved into 85.0 mL of dry diethyl ether. Sodium hydride (Aldrich) was rinsed thoroughly with hexanes and filtered prior to use to remove any mineral oil. Dry tetrahydrofuran (THF) and diethyl ether (Et2O) were obtained from Fisher as Optima grade and dried using a PPT Glass Contour Solvent Purification System, under argon, immediately prior to use, and kept under an inert atmosphere. Methods. The density and concentrations of the polymer samples were measured gravimetrically, as has been previously described.35 The concentrations of the MePEG7SO3H acid/ MePEGn copolymer mixtures were calculated by converting the mass of both the acid and the polymer to volume using their respective densities. Then, the mass of acid was converted to moles by using the acid’s molecular weight and was divided by the total volume of the acid plus polymer (this method specifically assumes that the volumes are additive). The viscosities of the polymer samples were measured using a Brookfield DV-III Ultra Programmable Rheometer. The CPE40 spindle was used and the viscosities measured under a flow of dry nitrogen at three different rotational speeds which were averaged. The rotational speeds were selected to keep the torque in a range of 10−100%. The samples were dried at 50 °C under a vacuum prior to measurement. Gel permeation chromatography (GPC) measurements were performed using two 30 cm PL Mixed-D analytical columns with a Polymer Laboratories ELS-2100 evaporative light scattering detector. Polystyrene molecular weight standards (PL-EasiCal PS-2, MW range 580−480 000) were used to calibrate the MW range prior to running unknown samples. THF was then allowed to elute through the column for 30 min to remove any remaining samples and to equilibrate the system. Unknown samples were made by dissolving 2−3 mg of sample in 1 g of THF. AC-impedance measurements were performed using a PAR 283 potentiostat equipped with a PerkinElmer 5210 lock-in amplifier.16 Conductivity is determined from a Nyquist plot by the diameter of the high frequency semicircle.36 NMR measurements were made with either a Bruker AC-300 or Bruker DRX-500 instrument. Strong acid ion exchange columns were prepared by placing 50 mL (95 mequiv) of Amberlite IR-120H ion-exchange resin (1.9 mequiv/mL) in a chromatography column with a porous frit. Hydrochloric acid (1 M, 300 mL, 300 mequiv) was allowed to flow through the column to exchange all of the cation sites to H+. Deionized water was then allowed to flow through the column until the pH of the column was near neutral pH (∼6.0−8.0). A strong base exchange column was similarly prepared with 50 mL (70 mequiv) of Amberlite IRA-400(Cl) strongly basic ion-exchange resin (1.4 mequiv/mL), followed by charging with sodium hydroxide (1 M, 225 mL, 225 mequiv), and rinsing with deionized water to a near neutral pH. Synthesis. Scheme 1 describes the synthesis of MePEG and MePPG polymers (4a−c) from MePEG7OH and MePPGnOH (1a−c). Samples with the “a” designation were prepared from the MePEG7OH as a starting material, while samples with the “b” and “c” designations were prepared from MePPG3OH and MePPG2OH, respectively. Table S1 (Supporting Information) summarizes preparation of the sol−gel copolymers. MePEG7 Allyl: (MePEG7OCH2CHCH2) (2a) was prepared as previously described.5,16,17
Scheme 1. Synthesis of MePEG/MePPG Polymer
Synthesis of Tri(propylene glycol) Allyl Methyl Ether (MePPG3OCH2CHCH2) (2b). MePPG3 allyl (2b; Scheme 1) was synthesized analogously to the method used to prepare 2a. Briefly, NaH (4.87 g, 202.9 mmol) was slurried with THF in an air-free round-bottom flask. MePPG3OH (20.91 g, 101.5 mmol) was dissolved in THF and added dropwise to the NaH/THF slurry. Allyl bromide (19.63 g, 162.2 mmol) was dissolved in THF and added dropwise to the reaction mixture. A clear viscous liquid (2b) was recovered (18.11 g, 73.6 mmol, 72.5% yield). NMR (1H, in CDCl3), δ (ppm): 1.1 (s, 9H), 3.27−3.41 (m, 9H), 3.99 (d, 2H), 5.12 (dd, 2H), 5.83 (m, 1H). NMR (13C, in CDCl3), δ (ppm): 17.02, 56.60, 58.98, 70.02, 72.89−75.85, 116.10, 135.45. Synthesis of Di(propylene glycol) Allyl Methyl Ether (MePPG2OCH2CHCH2) (2c). MePPG2 allyl (2c; Scheme 1) was synthesized according to the method used to prepare 2b using the following amounts: NaH (6.10g, 254.1 mmol), MePPG2OH (25.13 g, 169.6 mmol), and allyl bromide (40.00 g, 330.6 mmol). A clear viscous liquid (2c) was recovered (22.34 g, 118.7 mmol, 70.0% yield). NMR (1H, in CDCl3), δ (ppm): 1.16 (s, 6H), 3.34−3.62 (m, 6H), 4.07 (d, 2H), 5.21 (dd, 2H), 5.91 (m, 1H). NMR (13C, in CDCl3), δ (ppm): 17.35, 56.88, 59.25, 70.26, 73.19−76.05, 116.50, 135.48. MePEG7 Monomers: MePEG7OCH2CH2CH2Si(OEt)3 (3a) was prepared as previously described.5,16,17 Synthesis of MePPG3 Monomer (MePPG3OCH2CH2CH2Si(OEt)3) (3b). The MePPG3 monomer was prepared analogously to 3a using the following amounts: triethoxysilane (14.50 g, 88.4 mmol), 2b (18.11 g, 73.6 mmol), and Karstedt’s catalyst (∼80 μL). A clear viscous liquid (3b) was recovered (28.30 g, 69.0 mmol, 93.8% yield). NMR (1H, in CDCl3), δ (ppm): 0.57 (m, 2H), 1.07 (m, 9H), 1.17 (m, 9H), 1.58 (m, 2H), 3.29−3.54 (m, 9H), 3.80 (m, 6H). Synthesis of MePPG2 Monomer (MePPG2OCH2CH2CH2Si(OEt)3) (3c). MePPG2 monomer (3c) was prepared in the same manner as 3a using the following amounts: triethoxysilane (30.60 g, 186.6 mmol), 2c (22.34 g, 169.6 mmol), and Karstedt’s catalyst (∼80 μL). A clear viscous liquid (3c) was recovered (31.16 g, 88.5 mmol, 52.2% yield). NMR (1H, in CDCl3), δ (ppm): 0.56 (m, 2H), 1.07 (m, 6H), 1.16 (m, 9H), 1.60 (m, 2H), 3.25−3.54 (m. 6H), 3.76 (m, 6H). Synthesis of MePEG7 Polymer (MePEG7OCH2CH2CH2SiO1.5) (4a). The MePEG7 polymer (4a) was prepared as previously described.5,16,17 13004
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Table 1. Fractional Free Volumes for PEG−PPG Copolymers and MePEG7SO3H Acid polymers and copolymers MePEG7 polymer MePPG3 polymer MePPG2 polymer MePEG7/MePPG3 copolymer
MePEG7/MePPG2 copolymer
MePPG3/MePPG2 copolymer
MePEG7SO3H
75:25f 50:50 25:75 75:25 50:50 25:75 75:25 50:50 25:75
MWa (g/mol)
D (g/mL)
molar volume (Vm)b
van der Waals volume (Vw)c
FFVd
Vf,ethere
443 299 241 407 371 335 393 342 292 285 270 256 414
1.169 1.109 1.141 1.151 1.137 1.148 1.159 1.156 1.136 1.104 1.116 1.123 1.212
379 270 211 354 326 292 339 296 257 258 242 228 342
262 183 147 242 222 203 234 205 176 174 165 156 267
0.309 0.321 0.304 0.314 0.317 0.305 0.310 0.308 0.315 0.325 0.318 0.314 0.330
0.789 0.697 0.622 0.772 0.751 0.727 0.763 0.729 0.685 0.681 0.663 0.644 0.973
The effective MW for copolymers represents the MW of one “repeat unit” of the polymer. One repeat unit of MePEG7 polymer is defined as MePEG7OCH2CH2CH2SiO3/2. bVm for polymers and copolymers represents the weighted Vm calculated using the effective MW. cVw for polymers and copolymers represents the weighted Vw calculated by the Bondi group contribution method. dFractional free volume (FFV) is calculated according to eq 3. eThe calculation of the volume fraction of ether (Vf,ether) has been reported.17,20,37 fThe 75:25 ratio indicates that this copolymer is 75% mole fraction MePEG7 polymer and 25% mole fraction MePPG3 polymer (Table S1, Supporting Information). a
∼100 mTorr for 30 min. The resulting product was a clear and colorless viscous liquid. The integration of the 1H NMR trimethylsilyl peak at δ = 0.10 ppm was ratioed to the −OCH3 peak of the MePEG group, showing the presence of 5.7% uncondensed Si−OH groups in this polymer.
Synthesis of Sol−Gel Polymer (MePPG3OCH2CH2CH2SiO3/2) (4b). The MePPG3 polymer (4b) was prepared analogously to 4a using the following amounts: 3b (4.11 g, 10.0 mmol). The resulting gel 4b was a clear viscous liquid. Synthesis of Sol−Gel Polymer (MePPG2OCH2CH2CH2SiO3/2) (4c). The MePPG2 polymer (4c) was prepared in the same manner as the MePEG7 polymer (4a) using the following: 3c (4.38 g, 12.43 mmol). The resulting gel 4c was a clear viscous liquid. Synthesis of Sol−Gel Copolymers. The sol−gel copolymers were polymerized in the same way as the MePEG7 polymer (4a). Here, the two comonomers were mixed together and an excess (6 equiv) of slightly acidic water (pH ∼ 3, one drop of conc. HCl in 100 mL of distilled water) was added. The millimoles and mole fractions of the comonomers are summarized in Table S1 (Supporting Information). The solution was mixed well and allowed to hydrolyze at room temperature for 12−24 h. The excess water and ethanol were removed by rotary evaporation, and the resulting gel was placed in a vacuum oven at 60 °C for 24 h. Table S1 (Supporting Information) shows the GPC results for these copolymers. Synthesis of MePEG7SO3H Acid (MePEG7(CH2)3SO3H) was prepared as previously described.16,17,20−22,35,37 End Group Analysis. End group analysis was performed on all of the prepared copolymers to test for uncondensed Si−OH from the sol−gel condensation to form the polymers. Test samples were mixed with chlorotrimethylsilane, (CH3)3Si−Cl, with which the uncondensed −OH groups reacted with to label each residual OH group with a trimethylsilyl group. We then measured the labeled samples by NMR and ratioed the integrated peak areas of the trimethylsilyl groups and the terminal MePEG methyl groups to quantitate the amount of unreacted −OH groups per polymer unit. In one experiment, MePEG7 polymer (0.035 g, 0.079 mmol) was dissolved in 20 mL of toluene in an argon purged flask. Then, a large excess of chlorotrimethylsilane (0.5 mL, 4 mmol) was added. The reaction mixture was stirred for 6 h. Afterwards, 2.0 g of K2CO3 was added to quench any unreacted HCl and then stirred for 1 h. The solution was filtered, and the toluene and unreacted chlorotrimethylsilane (BP = 57 °C) was removed by rotary evaporation followed by evacuation to
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RESULTS AND DISCUSSION Fractional Free Volume (FFV). We have previously described how to determine the V w and FFV of a copolymer.20,24,26,27 The FFV data for our MePEG and MePPG polymers and their copolymers are shown in Table 1. The FFV values are based on the van der Waals volume as calculated by the Bondi group contribution method. These values are average values taken from many different sample types and generally have a small amount of error associated with them. However, due to the magnitude of the values, this error is much smaller than the differences in the values presented in Table 1. The density is also used in the calculation of FFV which was measured using a micro balance in triplicate. The error associated with these measurements is also insignificant to the tabulated values of FFV. In general, the MePPG3 polymer has greater FFV than the MePEG7 polymer, and the copolymerization of MePPG3 with the MePEG7 polymer leads to copolymers with greater FFV as compared to the MePEG7 polymer. While the differences in FFV seen in Table 1 appear to be small, we have found that these small differences in FFV can have a large effect on the ionic conductivity.20−22,37 We have also described how to calculate the volume fraction of PEG (Vf,PEG) of a copolymer.17,20,37 Note that we have previously called this term the volume fraction of PEG; however, we are also using polypropylene glycol in this paper; thus, we are switching our notation to the volume fraction of ether (Vf,ether).5,16,17 The mass and density both were used to calculate the Vf,ether of these polymers. The error associated with the density measurements, as stated above, is not significant. The masses were measured on a standard analytical balance whose mass is accurate to ±0.001 g; this is less than 0.01% of the masses of the samples measured and is also not significant. The Vf,ether data is also summarized in Table 1. Of note in these data is that several polymers have similar FFVs but very 13005
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Table 2. Ether Volume Fractions for PEG−PPG Copolymer Electrolyte Mixtures with 0.26 and 1.32 M MePEG7SO3H Acid polymer
[MePEG7SO3H] (mol/L)
Vf,ether,mixa
FFVmixb
0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32
0.452 0.455 0.446 0.454 0.441 0.453 0.450 0.454 0.449 0.454 0.448 0.454 0.450 0.454 0.448 0.454 0.445 0.454 0.445 0.454 0.444 0.454 0.443 0.454
0.309 0.316 0.322 0.324 0.306 0.314 0.315 0.320 0.318 0.322 0.307 0.315 0.312 0.318 0.310 0.317 0.316 0.320 0.325 0.326 0.319 0.322 0.316 0.320
MePEG7 polymer electrolyte MePPG3 polymer electrolyte MePPG2 polymer electrolyte MePEG7/MePPG3 copolymer electrolyte
75:25 50:50 25:75
MePEG7/MePPG2 copolymer electrolyte
75:25 50:50 25:75
MePPG3/MePPG2 copolymer electrolyte
75:25 50:50 25:75
a
Vf,ether,mix for copolymer electrolytes is the weighted Vf,ether,mix of the monomeric units and the MePEGSO3H acid. bFFVmix for copolymer electrolytes is the weighted FFVmix of the monomeric units and the MePEGSO3H acid.
Table 3. GPC Data for Copolymers with Weight Average Molecular Weight (Mw), Polydispersity Index (PDI), and Number of Monomers with the Percent Uncondensed Si−OH “high” MW peakc polymers and copolymers MePEG7 polymer MePPG3 polymer MePPG2 polymer MePEG7/MePPG3 copolymer
MePEG7/MePPG2 copolymer
MePPG3/MePPG2 copolymer
75:25 50:50 25:75 75:25 50:50 25:75 75:25 50:50 25:75
“low” MW peakd
Mw (Da)
PDIa
no. of monomersb
Mw (Da)
PDIa
no. of monomersb
% Si−OHe
3813 2652 3163 5017 4140 2794 4165 4166 3332 2191 2485 3813
1.37 2.43 8.01 1.53 1.51 4.70 1.46 1.61 1.52 4.57 2.98 3.06
8.61 8.86 13.1 12.3 11.2 8.33 10.6 12.2 11.4 7.69 9.20 14.4
546
1.31
1.23
550 577
1.55 1.50
1.35 1.55
527 539 450
1.60 1.26 1.52
1.34 1.58 1.54
1.00 2.30 1.78 1.44 4.74 4.96 1.19 1.19 5.07 1.07 1.96 1.19
PDI = Mw/Mn. bNo. of monomers is calculated by dividing Mw by the weighted monomer molecular weight. c“High” MW peak is the peak observed with the highest Mw when more than one peak is present. d“Low” MW peak is the peak observed with the lowest Mw when more than one peak is present. e% uncondensed Si−OH is equal to 1H NMR −OTMS divided by 3 Si−OH per monomer times 9 protons per TMS. a
different Vf,ether. For instance, the MePEG7 polymer, the MePPG2 polymer, and the MePEG7/MePPG2 copolymer all have a smaller variation in FFV (Table 1: 0.304−0.315, a 4% variation) but have a much larger variation in the range of the Vf,ether value (Table 1: 0.622−0.789, a 27% variation). It appears that in this system we have small variations in FFV but much larger variations in Vf,ether. We have probed the effect of FFV on the transport properties by incorporating bulky groups such as diphenyl siloxane and isobutyl siloxane.20 In this report, we are adding free volume using PPG groups that lower the volume fraction of conducting ethers. Thus, we are able to make a better comparison about the relative contributions of
fractional free volume and volume fraction of ether to the observed transport properties. The calculation of the volume fraction of ether in a mixture of MePEGnSO3H acid and MePEGn and MePPGn copolymers (Vf,ether,mix) has also been described previously.17,20,37 Table 2 shows the calculated values of the FFV and the volume fractions of ether in the copolymer/acid electrolyte mixtures. In the 1.32 M acid containing polymer electrolytes, Vf,ether,mix is dominated by the contributions of the added MePEG7SO3H acid. For the low concentration 0.26 M acid containing polymer electrolytes, Vf,ether,mix for the MePEG7 based polymers had larger values than the shorter MePPGn based polymers. In this 13006
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higher MePEG7 fractions. This more random polymerization is also consistent with a faster polymerization and an open-ended ladder geometry. End Group Analysis. End group analysis was performed to determine if the copolymers were completely condensed, and if the presence of the copolymer altered the degree of polymerization. The end group analysis results are also included in Table 3. The copolymers ranged from 1 to 5% uncondensed Si−OH. These relatively low numbers indicate that the condensation was nearly complete, as would be expected from a completely condensed T8 silsesquioxane cluster. The highest percentage of uncondensed silanols was in the copolymers with the highest fraction of PPG. These could be caused by size incompatibilities or differences in polymerization rates. Both occurrences would be expected to increase the amount of uncondensed silanols. Viscosity. The viscosities of the copolymers were measured to determine the relationship between fractional free volume and viscosity for these copolymers. The viscosity data taken at 25 °C is summarized in Table S1 (Supporting Information). The viscosity of the pure polymers decreases in the order MePPG2 < MePPG3 < MePEG7. We also see a similar decrease for the MePPG3/MePPG2 copolymers in the order 25% MePPG3 < 50% MePPG3 < 75% MePPG3. The viscosities of the MePPG3/MePPG2 copolymers follow the same trend as their calculated FFV values. However, in the heterocopolymers (MePEG 7 /MePPG 3 and MePEG 7 / MePPG2), the order of viscosity is 75% > 25% > 50%. This odd arrangement seems counterintuitive, but this trend is in fact following the calculated FFV trend. Figure 1 shows the Doolittle plot of all the copolymers at 25 °C. The best fit line for all of the data points together (i.e., the
case, the lower concentration of the MePEG7SO3H acid contributes a much smaller amount to the overall Vf,ether. Gel Permeation Chromatography (GPC). GPC analysis was performed to determine the effects of cross-linking in the polymerization of the MePEGn and MePPGn polymers and copolymers. Evidence of cross-linking and the degree of polymerization can be determined from GPC analysis from the mass and polydispersity index (PDI). The GPC analysis results for the MePEGn and MePPGn polymers and copolymers are summarized in Table 3. The GPC data allows us to predict the structure of our polymers based on the previous work of Ghosh et al.35 Two peaks were observed in the GPC for many of the copolymers that correspond to the polymer and dimer peaks. There is only one peak observed for several of the copolymers because the monomer and “dimer” of these copolymers have a small Mw. The ELS detector has difficulty detecting these low Mw components (ELS sensitivity ∝ MW2).17,20,37 For the polymers that have two peaks, there is a low molecular weight peak that corresponds to a mixture of monomers and dimers. For high MW peaks, the Mw, Mn, and PDI support the formation of T8 silsesquioxane clusters (Scheme S1, Supporting Information).35 In these high MW peaks, the number of monomer units ranges from approximately 8 to 15 for the high MW peaks. We have previously noted that the polystyrene MW standards used to obtain the Mw and Mn values appear to systematically underestimate the actual molecular weight of glycol based polymers by up to 40%.16 We did not use PEG based calibration standards so that our data would be comparable to other data for polymer electrolytes that use polystyrene calibration standards. In the low MW peaks, the Mw, Mn, and PDI support the formation of T2 dimer clusters where one silicon atom is connected to one other silicon atom with one or more Si−O−Si bonds. For both of the copolymers with the longer MePEG7 (i.e., the MePEG7/MePPG3 and MePEG7/MePPG2 copolymers), the number of monomer units in the high MW peak decreased as the mole fraction of PPG increased. This likely indicates the presence of incomplete T8 clusters (i.e., open T7 or T6 clusters; Scheme S1, Supporting Information). We have characterized the formation of these incomplete clusters in a previous publication.35 For the MePPG3/MePPG2 copolymers, the number of monomer units increased, perhaps indicating the presence of a ladder type structure. We also infer from these results that the rate of polymerization is greater for the MePPG polymers, and relatively slower for the MePEG polymer. The reaction was carried out for 12− 24 h so that the sol−gel reaction would complete hydrolysis of the ethoxy groups and reach equilibrium. The smaller MePPG2 and MePPG3 comonomers have less steric hindrance, which likely allows the condensation reaction to proceed faster than it does for the larger MePEG7 comonomer. It is also noteworthy that the MePPG2 had the highest number of monomer units in the high molecular weight peak, indicating that its polymerization rate is the fastest.38 Here a faster rate of polymerization may make a polymer more likely to adopt the ladder geometry than the T8 silsesquioxane geometry. For the polymers with the highest fraction of MePEG7, the PDI was between 1.3 and 1.6, indicating a small dispersity in the polymer’s molecular weight. The polymers with higher fractions of PPG, especially MePPG2, had considerably higher PDI values ranging from 2.4 to 8.0, indicating a much more random polymerization compared to those polymers with the
Figure 1. Doolittle plot for all MePEG/MePPG copolymers. The best fit linear line is shown for the MePPG3/MePPG2 copolymers (y = −2.2601x + 6.138, R2 = 0.983, p-value = 0.0009) and MePEG7/ MePPGx copolymers (y = −0.3294x + 0.3625, R2 = 0.0505, p-value = 0.628817).
pure polymers, heterocopolymers, and homocopolymers grouped together) had a poor R2 value (0.0063) and a high p-value (0.8059), indicating that there is no correlation between FFV and viscosity for these samples (note: the best fit for all the data is not shown in Figure 1). On further inspection, the linear fit of just the MePPG3/ MePPG2 homocopolymers (solid circles and solid line in Figure 1) yielded a very good R2 value (0.983) and a significant p-value 13007
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9). The linear best fit shown has a small slope, a very low R2 value (0.0030), and a large p-value (0.7966). These results clearly indicate that the Forsythe equation is not obeyed for this set of copolymers. This is an interesting lack of correlation, because we have previously observed a correlation between ionic conductivity and the volume fraction of PEG in a polymer, which we used as a proxy for free volume. This correlation, however, existed for MePEG based polymers and mixtures of MePEG based polymers.16,17 From our previous studies using the volume fraction of PEG, we understand that ionic conductivity results from the rearrangement of ether units. For this work, the Vf,PEG concept has been extended to include the ethers of PPG, making Vf,ether. In our heterocopolymers, both the MePEG and MePPG have repeating ether units, and can thus both participate in the overall ionic conductivity. Figure 3 shows a modified Forsythe
(0.0009), indicating that there is a strong relationship for these copolymers. Furthermore, when all of the MePEG/MePPG heterocopolymers were grouped together (i.e., both the MePEG7/MePPG2 copolymers and MePEG7/MePPG3 copolymers; open circles in Figure 1), the correlation again showed a much smaller slope, a poor R2 value (0.0505), and a high pvalue (0.6282). This indicates that the heterocopolymers with heteromonomers do not follow the Doolittle equation. There are two considerations to take into account. First, there is a clear mismatch of monomer sizes that may affect the viscosity, and second, there is also a great difference in the slopes (−2.26 and −0.329 for the MePPG homopolymers and MePEG7/MePPGx heterocopolymers) which, as mentioned above, is the material specific constant q in eq 7a. This result agrees with our previous results,20 where the Doolittle fit for heterogeneous copolymers showed only a moderate R2 value (0.5340), a low p-value (0.0020), and a shallow slope (−0.611). Those results indicated that the FFV and viscosity were correlated, but the moderate R2 and shallow slope suggest the correlation is not strong, and the low p-value indicates a significant correlation. The p-value is likely to be larger if the slope is small, and much more likely to be small with a larger slope; that is, it is harder for the correlation to occur randomly if the slope is larger. If this were the case, then the p-value may not be indicative of a correlation and the FFV and viscosity may only be moderately correlated for that set of heterogeneous copolymers. These taken together indicate that the structures of the different copolymers are significantly different (as mentioned above in the GPC and end group analysis discussion). That is, differences in reactivity and associational forces make the MePPG/MePPG homocopolymers have a different structure from the MePEG/MePPG heteropolymers. Also, this difference in structure results in a significant difference in the transport properties of the MePEG/MePPG heterocopolymers. Ionic Conductivity. The ionic conductivities of the copolymers were measured to determine the relationship between ionic conductivity and FFV for these copolymers. Figure 2 shows a Forsythe plot correlating the molar equivalent ionic conductivity (Λ) with the inverse of FFV for all copolymers at 25 °C according to the Forsythe equation (eq
Figure 3. Forsythe plot with volume fraction of ether (Vf,ether) for all MePEG7/MePPGx copolymers with the best fit linear line shown. y = −13.1827x − 9.2248, R2 = 0.6146, p-value < 0.00001.
plot with molar equivalent conductivity (Λ) correlated with Vf,ether (instead of FFV) for all copolymers at 25 °C. The linear best fit shown has a much greater slope than the Forsythe correlation with FFV shown in Figure 2. In addition, the correlation in Figure 3 has a much greater R2 value (0.6146) and a small p-value (
Volume Fraction of Ether Is a Significant Factor in Controlling Conductivity in Proton Conducting Polyether Based Polymer Sol−Gel Electrolytes Benjamin Yancey, Jonathan Jones, and Jason E. Ritchie* Department of Chemistry and Biochemistry, The University of Mississippi, 222 Coulter Hall, University, Mississippi 38677, United States S Supporting Information *
ABSTRACT: We have synthesized several copolymers of methyl polyethylene glycol siloxane (MePEG7SiO3)m and methyl polypropylene glycol siloxane (MePPGnSiO3)m as hydrogen ion (H+) conducting polymer electrolytes. These copolymers were prepared by a sol−gel polymerization of mixtures of the MePEG and MePPG monomers. We synthesized these H+ conducting polymer electrolytes in order to study the relationship between observed ionic conductivity and structural properties such as viscosity, fractional free volume, and volume fraction of ether. We found that viscosity increased as the fraction of the smaller comonomer increased. For the MePPG2/MePPG3 copolymer, an increase in fractional free volume increased the fluidity. The heterogeneous copolymers (PEG/PPG copolymers) obeyed the Doolittle equation, while the homogeneous (PEG/PEG and PPG/PPG) copolymers did not. The increase of FFV did not, however, correspond to an increase in conductivity, as would have been predicted by the Forsythe equation. The conductivity data did correspond to a modified Forsythe equation substituting Volume Fraction of Ether (Vf,ether) for FFV. We conclude that the proton conductivity of MePEG copolymers is more dependent on the volume fraction of ether than on the fractional free volume.
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INTRODUCTION Proton exchange membrane fuel cells (PEMFCs) use a polymer electrolyte to both physically separate the anode from the cathode and conduct hydrogen ions (H+) between the electrodes. Polymer electrolytes have the advantage of being easy to chemically modify, and have properties that support ion mobility as well as mechanical durability.1−3 Currently, Nafion, a sulfonated perfluorinated polymer, is the most widely used proton conducting polymer electrolyte. Nafion has the necessary chemical stability, mechanical properties, and ionic conductivity when hydrated for use in a PEM fuel cell. The major disadvantages of Nafion are its cost, poor hydrophobicity, and hydration dependent conductivity. Alternatively, membranes based on polybenzimidazole (PBI) and phosphoric acid have also been developed with an eye toward higher temperatures without the same water management requirements of Nafion. The hydration dependent ionic conductivity in Nafion limits the operational temperature to below 80 °C.4 The platinum catalytic anode in a PEMFC has a low resistance to CO poisoning (which is commonly present in H2 fuel streams produced from reforming of fossil fuels). These disadvantages necessitate the development of new anhydrous polymer electrolytes for PEM fuel cells, for which the U.S. Department of Energy has set an operational goal of 0.1 S/cm conductivity at 120 °C and 50% relative humidity. Polyethylene glycol (PEG) and poly(ethylene oxide) (PEO), and the related polymer polypropylene glycol (PPG), conduct © 2014 American Chemical Society
small cations in the absence of water. Neither PEG nor PPG have the mechanical stability required to serve as a fuel cell membrane. However, attachment of PEG or PPG groups to an inorganic matrix can form a hybrid organic/inorganic material combining the mechanical properties of the inorganic portion with the anhydrous conductivity of PEG and PPG.5−12 Siloxanes are easy to functionalize, and are chemically and mechanically stable, due to their chemical similarities to silica.13−15 Both PEG and PPG can be coupled to siloxanes by hydrosilylation reactions to form the inorganic/organic hybrid.5,16−22 Siloxane polymers are easily made from the acid catalyzed, sol−gel condensation of chlorosilanes or alkoxysilanes. Polymers formed by this condensation can exhibit the advantages of both the organic and inorganic portions, making them useful as polymer electrolytes. We are interested in how the structure of the polymer electrolyte affects the ionic conductivity. In terms of studying the structure, we look to intrinsic properties of the polymer including viscosity, ionic conductivity, fractional free volume, and volume fraction of the ionically conductive ether component (i.e., either the PEG or PPG units). Free volume theory is used to statistically evaluate glassy or amorphous polymer systems.23 The free volume (vf) is defined as the virtual volume of the molecule (the total volume Received: July 18, 2014 Revised: October 14, 2014 Published: October 14, 2014 13002
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indirectly occupied through random molecular motions, vm) minus the hard sphere volume (van der Waals volume, vw) of the molecule.23−25 Free volume is a scalar quantity that is dependent on the sample size of the material but can be expressed as the sample size independent: molar free volume (Vf, eq 1). When calculating the free volume of a polymer, the molar volume (Vm, eq 2) is first calculated using the density and molecular weight of the molecule, and then, the molar van der Waals volume (Vw) is calculated using the group contribution method developed by Bondi.24,26,27 Further, the fractional free volume (FFV, eq 3) is very useful in describing transport behavior in these systems, and is expressed as the ratio of molar free volume (Vf) to total molar volume (Vm). Fractional free volume is independent of sample geometry and volume and is useful for comparing the free volume of different materials.24,26,27 Vf = Vm − Vw
(1)
MW Vm = d
(2)
(V − Vw ) V FFV = f = m Vm Vm
(3)
Fractional Walden’s Rule: Ληα = constant
Doolittle developed an empirical equation (eq 7) to describe the relationship between free volume and viscosity.29,33 Doolittle’s relationship demonstrates that a smaller fractional free volume results in a smaller fluidity. In eq 7, A and q are material specific constants where A represents the fluidity extrapolated to zero free volume and q is a measure of the liquid’s intermolecular forces. In addition, Vm and Vf are the total molar volume and molar free volume, respectively. The ratio Vm/Vf is equivalent to the inverse fractional free volume (FFV−1), and substitution results in eq 7a. Doolittle’s Equation:
⎡ V ⎤ 1 = A exp⎢ −q m ⎥ η ⎣ Vf ⎦ ⎡ −q ⎤ 1 = A exp⎢ ⎣ FFV ⎥⎦ η
Dphys
F2 [z+2D+C+ + z −2D−C −] RT
⎡ γ ⎤ D = A exp⎢ − ⎣ FFV ⎥⎦
(8)
Forsythe Equation:
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⎛ ACF 2Z2 ⎞ ⎡ −γ ⎤ σ=⎜ ⎟ exp⎢ ⎣ FFV ⎥⎦ ⎝ RT ⎠
(9)
EXPERIMENTAL SECTION Materials. Polyethylene glycol monomethyl ether (CH3(OCH2CH2)nOH = MePEGnOH, Mn = 350, n = 7.24; Aldrich) and polypropylene glycol monomethyl ether (CH3(OCH(CH3)−CH2)nOH = MePPGnOH, Mn = 148.2, 206.3, n = 2, 3; Aldrich) were dried at 60 °C under a vacuum for approximately 24 h prior to use. This paper will refer to poly(ethylene glycol) monomethyl ether Mn = 350 as MePEG7OH, tri(propylene glycol) monomethyl ether Mn = 206.3 as MePPG3OH, and di(propylene glycol) monomethyl ether Mn = 148.2 as MePPG2OH. Copolymers of MePEG7 and MePPG3 will be referred to as MePEG7/MePPG3, MePEG7 and MePPG2 copolymers as MePEG7/MePPG2, and MePPG3 and MePPG2 copolymers as MePPG3/MePPG2. Triethoxysilane (Aldrich), allyl bromide (Acros), Karstedt’s catalyst (platinum(0)-1,3-divinyl-1,1,3,3-tetramethyldisiloxane complex solution in xylene, Pt ∼2%; Aldrich), and sodium sulfite (Fisher) were all used as received. Amberlite IRA400(Cl) anion exchange resin (Aldrich) and Amberlite IR-
(4)
(5)
Walden’s rule (eq 6a) defines the relationship between fluidity and conductivity. In this equation, Λ is the molar equivalent conductivity and η is the viscosity. This rule generally holds true for ideal solutions in which there are no ion−ion interactions. However, in real electrolyte solutions, the fractional Walden rule (eq 6b) is a better descriptor of real physical observations.31,32 In eq 6b, α is a constant between 0 and 1, with α = 1 representing ideal behavior (eq 6a); that is, viscosity is the only force impeding ionic mobility. Where 0 < α < 1, other forces are present that impede ionic mobility. Walden’s Rule: Λη = constant
(7a)
Cohen−Turnbull Equation:
Nernst−Einstein Equation: σION =
(7)
Cohen and Turnbull combined the Stokes−Einstein equation (eq 4) with the Doolittle equation (eq 7), resulting in the Cohen−Turnbull equation (eq 8). In this equation, A incorporates all of the constants in eq 4 and γ is the same as q in the Doolittle equation.25 The Cohen−Turnbull equation illustrates that, as the fractional free volume increases, the diffusion coefficient will also increase. Forsythe combined the Nernst−Einstein equation (eq 5) with the Cohen−Turnbull equation (eq 8), resulting in the Forsythe equation (eq 9).34 The Forsythe equation shows that, when the fractional free volume is increased, the ionic conductivity (σ) should increase as well.
In free volume theory, the transport properties of a material (e.g., viscosity - η, conductivity - σ, and diffusion coefficient D) are dependent on the free volume.28,29 For example, diffusion through a material is described as translation through openings in the free volume in a particle’s vicinity.25 Free volume, in this description, is a measure of the concentration of void space in a material. The Stokes−Einstein equation (eq 4) predicts that an increase in fluidity (fluidity = η−1) will result in an increase in the diffusion coefficient (D). The Nernst−Einstein equation (eq 5) predicts that an increase in the diffusion coefficient of either ion results in a proportional increase in the ionic conductivity.30 Equations 4 and 5 together indicate that an increase in the fluidity will cause an increase in the ionic conductivity. Stokes−Einstein Equation:
kT = 6πηRH
(6b)
(6a) 13003
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120H cation exchange resin (Aldrich) were used as received. Phosphorus tribromide (99%; Aldrich) was prepared as a 1.98 M solution in dry diethyl ether using 55.91 g of phosphorus tribromide dissolved into 85.0 mL of dry diethyl ether. Sodium hydride (Aldrich) was rinsed thoroughly with hexanes and filtered prior to use to remove any mineral oil. Dry tetrahydrofuran (THF) and diethyl ether (Et2O) were obtained from Fisher as Optima grade and dried using a PPT Glass Contour Solvent Purification System, under argon, immediately prior to use, and kept under an inert atmosphere. Methods. The density and concentrations of the polymer samples were measured gravimetrically, as has been previously described.35 The concentrations of the MePEG7SO3H acid/ MePEGn copolymer mixtures were calculated by converting the mass of both the acid and the polymer to volume using their respective densities. Then, the mass of acid was converted to moles by using the acid’s molecular weight and was divided by the total volume of the acid plus polymer (this method specifically assumes that the volumes are additive). The viscosities of the polymer samples were measured using a Brookfield DV-III Ultra Programmable Rheometer. The CPE40 spindle was used and the viscosities measured under a flow of dry nitrogen at three different rotational speeds which were averaged. The rotational speeds were selected to keep the torque in a range of 10−100%. The samples were dried at 50 °C under a vacuum prior to measurement. Gel permeation chromatography (GPC) measurements were performed using two 30 cm PL Mixed-D analytical columns with a Polymer Laboratories ELS-2100 evaporative light scattering detector. Polystyrene molecular weight standards (PL-EasiCal PS-2, MW range 580−480 000) were used to calibrate the MW range prior to running unknown samples. THF was then allowed to elute through the column for 30 min to remove any remaining samples and to equilibrate the system. Unknown samples were made by dissolving 2−3 mg of sample in 1 g of THF. AC-impedance measurements were performed using a PAR 283 potentiostat equipped with a PerkinElmer 5210 lock-in amplifier.16 Conductivity is determined from a Nyquist plot by the diameter of the high frequency semicircle.36 NMR measurements were made with either a Bruker AC-300 or Bruker DRX-500 instrument. Strong acid ion exchange columns were prepared by placing 50 mL (95 mequiv) of Amberlite IR-120H ion-exchange resin (1.9 mequiv/mL) in a chromatography column with a porous frit. Hydrochloric acid (1 M, 300 mL, 300 mequiv) was allowed to flow through the column to exchange all of the cation sites to H+. Deionized water was then allowed to flow through the column until the pH of the column was near neutral pH (∼6.0−8.0). A strong base exchange column was similarly prepared with 50 mL (70 mequiv) of Amberlite IRA-400(Cl) strongly basic ion-exchange resin (1.4 mequiv/mL), followed by charging with sodium hydroxide (1 M, 225 mL, 225 mequiv), and rinsing with deionized water to a near neutral pH. Synthesis. Scheme 1 describes the synthesis of MePEG and MePPG polymers (4a−c) from MePEG7OH and MePPGnOH (1a−c). Samples with the “a” designation were prepared from the MePEG7OH as a starting material, while samples with the “b” and “c” designations were prepared from MePPG3OH and MePPG2OH, respectively. Table S1 (Supporting Information) summarizes preparation of the sol−gel copolymers. MePEG7 Allyl: (MePEG7OCH2CHCH2) (2a) was prepared as previously described.5,16,17
Scheme 1. Synthesis of MePEG/MePPG Polymer
Synthesis of Tri(propylene glycol) Allyl Methyl Ether (MePPG3OCH2CHCH2) (2b). MePPG3 allyl (2b; Scheme 1) was synthesized analogously to the method used to prepare 2a. Briefly, NaH (4.87 g, 202.9 mmol) was slurried with THF in an air-free round-bottom flask. MePPG3OH (20.91 g, 101.5 mmol) was dissolved in THF and added dropwise to the NaH/THF slurry. Allyl bromide (19.63 g, 162.2 mmol) was dissolved in THF and added dropwise to the reaction mixture. A clear viscous liquid (2b) was recovered (18.11 g, 73.6 mmol, 72.5% yield). NMR (1H, in CDCl3), δ (ppm): 1.1 (s, 9H), 3.27−3.41 (m, 9H), 3.99 (d, 2H), 5.12 (dd, 2H), 5.83 (m, 1H). NMR (13C, in CDCl3), δ (ppm): 17.02, 56.60, 58.98, 70.02, 72.89−75.85, 116.10, 135.45. Synthesis of Di(propylene glycol) Allyl Methyl Ether (MePPG2OCH2CHCH2) (2c). MePPG2 allyl (2c; Scheme 1) was synthesized according to the method used to prepare 2b using the following amounts: NaH (6.10g, 254.1 mmol), MePPG2OH (25.13 g, 169.6 mmol), and allyl bromide (40.00 g, 330.6 mmol). A clear viscous liquid (2c) was recovered (22.34 g, 118.7 mmol, 70.0% yield). NMR (1H, in CDCl3), δ (ppm): 1.16 (s, 6H), 3.34−3.62 (m, 6H), 4.07 (d, 2H), 5.21 (dd, 2H), 5.91 (m, 1H). NMR (13C, in CDCl3), δ (ppm): 17.35, 56.88, 59.25, 70.26, 73.19−76.05, 116.50, 135.48. MePEG7 Monomers: MePEG7OCH2CH2CH2Si(OEt)3 (3a) was prepared as previously described.5,16,17 Synthesis of MePPG3 Monomer (MePPG3OCH2CH2CH2Si(OEt)3) (3b). The MePPG3 monomer was prepared analogously to 3a using the following amounts: triethoxysilane (14.50 g, 88.4 mmol), 2b (18.11 g, 73.6 mmol), and Karstedt’s catalyst (∼80 μL). A clear viscous liquid (3b) was recovered (28.30 g, 69.0 mmol, 93.8% yield). NMR (1H, in CDCl3), δ (ppm): 0.57 (m, 2H), 1.07 (m, 9H), 1.17 (m, 9H), 1.58 (m, 2H), 3.29−3.54 (m, 9H), 3.80 (m, 6H). Synthesis of MePPG2 Monomer (MePPG2OCH2CH2CH2Si(OEt)3) (3c). MePPG2 monomer (3c) was prepared in the same manner as 3a using the following amounts: triethoxysilane (30.60 g, 186.6 mmol), 2c (22.34 g, 169.6 mmol), and Karstedt’s catalyst (∼80 μL). A clear viscous liquid (3c) was recovered (31.16 g, 88.5 mmol, 52.2% yield). NMR (1H, in CDCl3), δ (ppm): 0.56 (m, 2H), 1.07 (m, 6H), 1.16 (m, 9H), 1.60 (m, 2H), 3.25−3.54 (m. 6H), 3.76 (m, 6H). Synthesis of MePEG7 Polymer (MePEG7OCH2CH2CH2SiO1.5) (4a). The MePEG7 polymer (4a) was prepared as previously described.5,16,17 13004
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Table 1. Fractional Free Volumes for PEG−PPG Copolymers and MePEG7SO3H Acid polymers and copolymers MePEG7 polymer MePPG3 polymer MePPG2 polymer MePEG7/MePPG3 copolymer
MePEG7/MePPG2 copolymer
MePPG3/MePPG2 copolymer
MePEG7SO3H
75:25f 50:50 25:75 75:25 50:50 25:75 75:25 50:50 25:75
MWa (g/mol)
D (g/mL)
molar volume (Vm)b
van der Waals volume (Vw)c
FFVd
Vf,ethere
443 299 241 407 371 335 393 342 292 285 270 256 414
1.169 1.109 1.141 1.151 1.137 1.148 1.159 1.156 1.136 1.104 1.116 1.123 1.212
379 270 211 354 326 292 339 296 257 258 242 228 342
262 183 147 242 222 203 234 205 176 174 165 156 267
0.309 0.321 0.304 0.314 0.317 0.305 0.310 0.308 0.315 0.325 0.318 0.314 0.330
0.789 0.697 0.622 0.772 0.751 0.727 0.763 0.729 0.685 0.681 0.663 0.644 0.973
The effective MW for copolymers represents the MW of one “repeat unit” of the polymer. One repeat unit of MePEG7 polymer is defined as MePEG7OCH2CH2CH2SiO3/2. bVm for polymers and copolymers represents the weighted Vm calculated using the effective MW. cVw for polymers and copolymers represents the weighted Vw calculated by the Bondi group contribution method. dFractional free volume (FFV) is calculated according to eq 3. eThe calculation of the volume fraction of ether (Vf,ether) has been reported.17,20,37 fThe 75:25 ratio indicates that this copolymer is 75% mole fraction MePEG7 polymer and 25% mole fraction MePPG3 polymer (Table S1, Supporting Information). a
∼100 mTorr for 30 min. The resulting product was a clear and colorless viscous liquid. The integration of the 1H NMR trimethylsilyl peak at δ = 0.10 ppm was ratioed to the −OCH3 peak of the MePEG group, showing the presence of 5.7% uncondensed Si−OH groups in this polymer.
Synthesis of Sol−Gel Polymer (MePPG3OCH2CH2CH2SiO3/2) (4b). The MePPG3 polymer (4b) was prepared analogously to 4a using the following amounts: 3b (4.11 g, 10.0 mmol). The resulting gel 4b was a clear viscous liquid. Synthesis of Sol−Gel Polymer (MePPG2OCH2CH2CH2SiO3/2) (4c). The MePPG2 polymer (4c) was prepared in the same manner as the MePEG7 polymer (4a) using the following: 3c (4.38 g, 12.43 mmol). The resulting gel 4c was a clear viscous liquid. Synthesis of Sol−Gel Copolymers. The sol−gel copolymers were polymerized in the same way as the MePEG7 polymer (4a). Here, the two comonomers were mixed together and an excess (6 equiv) of slightly acidic water (pH ∼ 3, one drop of conc. HCl in 100 mL of distilled water) was added. The millimoles and mole fractions of the comonomers are summarized in Table S1 (Supporting Information). The solution was mixed well and allowed to hydrolyze at room temperature for 12−24 h. The excess water and ethanol were removed by rotary evaporation, and the resulting gel was placed in a vacuum oven at 60 °C for 24 h. Table S1 (Supporting Information) shows the GPC results for these copolymers. Synthesis of MePEG7SO3H Acid (MePEG7(CH2)3SO3H) was prepared as previously described.16,17,20−22,35,37 End Group Analysis. End group analysis was performed on all of the prepared copolymers to test for uncondensed Si−OH from the sol−gel condensation to form the polymers. Test samples were mixed with chlorotrimethylsilane, (CH3)3Si−Cl, with which the uncondensed −OH groups reacted with to label each residual OH group with a trimethylsilyl group. We then measured the labeled samples by NMR and ratioed the integrated peak areas of the trimethylsilyl groups and the terminal MePEG methyl groups to quantitate the amount of unreacted −OH groups per polymer unit. In one experiment, MePEG7 polymer (0.035 g, 0.079 mmol) was dissolved in 20 mL of toluene in an argon purged flask. Then, a large excess of chlorotrimethylsilane (0.5 mL, 4 mmol) was added. The reaction mixture was stirred for 6 h. Afterwards, 2.0 g of K2CO3 was added to quench any unreacted HCl and then stirred for 1 h. The solution was filtered, and the toluene and unreacted chlorotrimethylsilane (BP = 57 °C) was removed by rotary evaporation followed by evacuation to
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RESULTS AND DISCUSSION Fractional Free Volume (FFV). We have previously described how to determine the V w and FFV of a copolymer.20,24,26,27 The FFV data for our MePEG and MePPG polymers and their copolymers are shown in Table 1. The FFV values are based on the van der Waals volume as calculated by the Bondi group contribution method. These values are average values taken from many different sample types and generally have a small amount of error associated with them. However, due to the magnitude of the values, this error is much smaller than the differences in the values presented in Table 1. The density is also used in the calculation of FFV which was measured using a micro balance in triplicate. The error associated with these measurements is also insignificant to the tabulated values of FFV. In general, the MePPG3 polymer has greater FFV than the MePEG7 polymer, and the copolymerization of MePPG3 with the MePEG7 polymer leads to copolymers with greater FFV as compared to the MePEG7 polymer. While the differences in FFV seen in Table 1 appear to be small, we have found that these small differences in FFV can have a large effect on the ionic conductivity.20−22,37 We have also described how to calculate the volume fraction of PEG (Vf,PEG) of a copolymer.17,20,37 Note that we have previously called this term the volume fraction of PEG; however, we are also using polypropylene glycol in this paper; thus, we are switching our notation to the volume fraction of ether (Vf,ether).5,16,17 The mass and density both were used to calculate the Vf,ether of these polymers. The error associated with the density measurements, as stated above, is not significant. The masses were measured on a standard analytical balance whose mass is accurate to ±0.001 g; this is less than 0.01% of the masses of the samples measured and is also not significant. The Vf,ether data is also summarized in Table 1. Of note in these data is that several polymers have similar FFVs but very 13005
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Table 2. Ether Volume Fractions for PEG−PPG Copolymer Electrolyte Mixtures with 0.26 and 1.32 M MePEG7SO3H Acid polymer
[MePEG7SO3H] (mol/L)
Vf,ether,mixa
FFVmixb
0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32 0.26 1.32
0.452 0.455 0.446 0.454 0.441 0.453 0.450 0.454 0.449 0.454 0.448 0.454 0.450 0.454 0.448 0.454 0.445 0.454 0.445 0.454 0.444 0.454 0.443 0.454
0.309 0.316 0.322 0.324 0.306 0.314 0.315 0.320 0.318 0.322 0.307 0.315 0.312 0.318 0.310 0.317 0.316 0.320 0.325 0.326 0.319 0.322 0.316 0.320
MePEG7 polymer electrolyte MePPG3 polymer electrolyte MePPG2 polymer electrolyte MePEG7/MePPG3 copolymer electrolyte
75:25 50:50 25:75
MePEG7/MePPG2 copolymer electrolyte
75:25 50:50 25:75
MePPG3/MePPG2 copolymer electrolyte
75:25 50:50 25:75
a
Vf,ether,mix for copolymer electrolytes is the weighted Vf,ether,mix of the monomeric units and the MePEGSO3H acid. bFFVmix for copolymer electrolytes is the weighted FFVmix of the monomeric units and the MePEGSO3H acid.
Table 3. GPC Data for Copolymers with Weight Average Molecular Weight (Mw), Polydispersity Index (PDI), and Number of Monomers with the Percent Uncondensed Si−OH “high” MW peakc polymers and copolymers MePEG7 polymer MePPG3 polymer MePPG2 polymer MePEG7/MePPG3 copolymer
MePEG7/MePPG2 copolymer
MePPG3/MePPG2 copolymer
75:25 50:50 25:75 75:25 50:50 25:75 75:25 50:50 25:75
“low” MW peakd
Mw (Da)
PDIa
no. of monomersb
Mw (Da)
PDIa
no. of monomersb
% Si−OHe
3813 2652 3163 5017 4140 2794 4165 4166 3332 2191 2485 3813
1.37 2.43 8.01 1.53 1.51 4.70 1.46 1.61 1.52 4.57 2.98 3.06
8.61 8.86 13.1 12.3 11.2 8.33 10.6 12.2 11.4 7.69 9.20 14.4
546
1.31
1.23
550 577
1.55 1.50
1.35 1.55
527 539 450
1.60 1.26 1.52
1.34 1.58 1.54
1.00 2.30 1.78 1.44 4.74 4.96 1.19 1.19 5.07 1.07 1.96 1.19
PDI = Mw/Mn. bNo. of monomers is calculated by dividing Mw by the weighted monomer molecular weight. c“High” MW peak is the peak observed with the highest Mw when more than one peak is present. d“Low” MW peak is the peak observed with the lowest Mw when more than one peak is present. e% uncondensed Si−OH is equal to 1H NMR −OTMS divided by 3 Si−OH per monomer times 9 protons per TMS. a
different Vf,ether. For instance, the MePEG7 polymer, the MePPG2 polymer, and the MePEG7/MePPG2 copolymer all have a smaller variation in FFV (Table 1: 0.304−0.315, a 4% variation) but have a much larger variation in the range of the Vf,ether value (Table 1: 0.622−0.789, a 27% variation). It appears that in this system we have small variations in FFV but much larger variations in Vf,ether. We have probed the effect of FFV on the transport properties by incorporating bulky groups such as diphenyl siloxane and isobutyl siloxane.20 In this report, we are adding free volume using PPG groups that lower the volume fraction of conducting ethers. Thus, we are able to make a better comparison about the relative contributions of
fractional free volume and volume fraction of ether to the observed transport properties. The calculation of the volume fraction of ether in a mixture of MePEGnSO3H acid and MePEGn and MePPGn copolymers (Vf,ether,mix) has also been described previously.17,20,37 Table 2 shows the calculated values of the FFV and the volume fractions of ether in the copolymer/acid electrolyte mixtures. In the 1.32 M acid containing polymer electrolytes, Vf,ether,mix is dominated by the contributions of the added MePEG7SO3H acid. For the low concentration 0.26 M acid containing polymer electrolytes, Vf,ether,mix for the MePEG7 based polymers had larger values than the shorter MePPGn based polymers. In this 13006
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higher MePEG7 fractions. This more random polymerization is also consistent with a faster polymerization and an open-ended ladder geometry. End Group Analysis. End group analysis was performed to determine if the copolymers were completely condensed, and if the presence of the copolymer altered the degree of polymerization. The end group analysis results are also included in Table 3. The copolymers ranged from 1 to 5% uncondensed Si−OH. These relatively low numbers indicate that the condensation was nearly complete, as would be expected from a completely condensed T8 silsesquioxane cluster. The highest percentage of uncondensed silanols was in the copolymers with the highest fraction of PPG. These could be caused by size incompatibilities or differences in polymerization rates. Both occurrences would be expected to increase the amount of uncondensed silanols. Viscosity. The viscosities of the copolymers were measured to determine the relationship between fractional free volume and viscosity for these copolymers. The viscosity data taken at 25 °C is summarized in Table S1 (Supporting Information). The viscosity of the pure polymers decreases in the order MePPG2 < MePPG3 < MePEG7. We also see a similar decrease for the MePPG3/MePPG2 copolymers in the order 25% MePPG3 < 50% MePPG3 < 75% MePPG3. The viscosities of the MePPG3/MePPG2 copolymers follow the same trend as their calculated FFV values. However, in the heterocopolymers (MePEG 7 /MePPG 3 and MePEG 7 / MePPG2), the order of viscosity is 75% > 25% > 50%. This odd arrangement seems counterintuitive, but this trend is in fact following the calculated FFV trend. Figure 1 shows the Doolittle plot of all the copolymers at 25 °C. The best fit line for all of the data points together (i.e., the
case, the lower concentration of the MePEG7SO3H acid contributes a much smaller amount to the overall Vf,ether. Gel Permeation Chromatography (GPC). GPC analysis was performed to determine the effects of cross-linking in the polymerization of the MePEGn and MePPGn polymers and copolymers. Evidence of cross-linking and the degree of polymerization can be determined from GPC analysis from the mass and polydispersity index (PDI). The GPC analysis results for the MePEGn and MePPGn polymers and copolymers are summarized in Table 3. The GPC data allows us to predict the structure of our polymers based on the previous work of Ghosh et al.35 Two peaks were observed in the GPC for many of the copolymers that correspond to the polymer and dimer peaks. There is only one peak observed for several of the copolymers because the monomer and “dimer” of these copolymers have a small Mw. The ELS detector has difficulty detecting these low Mw components (ELS sensitivity ∝ MW2).17,20,37 For the polymers that have two peaks, there is a low molecular weight peak that corresponds to a mixture of monomers and dimers. For high MW peaks, the Mw, Mn, and PDI support the formation of T8 silsesquioxane clusters (Scheme S1, Supporting Information).35 In these high MW peaks, the number of monomer units ranges from approximately 8 to 15 for the high MW peaks. We have previously noted that the polystyrene MW standards used to obtain the Mw and Mn values appear to systematically underestimate the actual molecular weight of glycol based polymers by up to 40%.16 We did not use PEG based calibration standards so that our data would be comparable to other data for polymer electrolytes that use polystyrene calibration standards. In the low MW peaks, the Mw, Mn, and PDI support the formation of T2 dimer clusters where one silicon atom is connected to one other silicon atom with one or more Si−O−Si bonds. For both of the copolymers with the longer MePEG7 (i.e., the MePEG7/MePPG3 and MePEG7/MePPG2 copolymers), the number of monomer units in the high MW peak decreased as the mole fraction of PPG increased. This likely indicates the presence of incomplete T8 clusters (i.e., open T7 or T6 clusters; Scheme S1, Supporting Information). We have characterized the formation of these incomplete clusters in a previous publication.35 For the MePPG3/MePPG2 copolymers, the number of monomer units increased, perhaps indicating the presence of a ladder type structure. We also infer from these results that the rate of polymerization is greater for the MePPG polymers, and relatively slower for the MePEG polymer. The reaction was carried out for 12− 24 h so that the sol−gel reaction would complete hydrolysis of the ethoxy groups and reach equilibrium. The smaller MePPG2 and MePPG3 comonomers have less steric hindrance, which likely allows the condensation reaction to proceed faster than it does for the larger MePEG7 comonomer. It is also noteworthy that the MePPG2 had the highest number of monomer units in the high molecular weight peak, indicating that its polymerization rate is the fastest.38 Here a faster rate of polymerization may make a polymer more likely to adopt the ladder geometry than the T8 silsesquioxane geometry. For the polymers with the highest fraction of MePEG7, the PDI was between 1.3 and 1.6, indicating a small dispersity in the polymer’s molecular weight. The polymers with higher fractions of PPG, especially MePPG2, had considerably higher PDI values ranging from 2.4 to 8.0, indicating a much more random polymerization compared to those polymers with the
Figure 1. Doolittle plot for all MePEG/MePPG copolymers. The best fit linear line is shown for the MePPG3/MePPG2 copolymers (y = −2.2601x + 6.138, R2 = 0.983, p-value = 0.0009) and MePEG7/ MePPGx copolymers (y = −0.3294x + 0.3625, R2 = 0.0505, p-value = 0.628817).
pure polymers, heterocopolymers, and homocopolymers grouped together) had a poor R2 value (0.0063) and a high p-value (0.8059), indicating that there is no correlation between FFV and viscosity for these samples (note: the best fit for all the data is not shown in Figure 1). On further inspection, the linear fit of just the MePPG3/ MePPG2 homocopolymers (solid circles and solid line in Figure 1) yielded a very good R2 value (0.983) and a significant p-value 13007
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9). The linear best fit shown has a small slope, a very low R2 value (0.0030), and a large p-value (0.7966). These results clearly indicate that the Forsythe equation is not obeyed for this set of copolymers. This is an interesting lack of correlation, because we have previously observed a correlation between ionic conductivity and the volume fraction of PEG in a polymer, which we used as a proxy for free volume. This correlation, however, existed for MePEG based polymers and mixtures of MePEG based polymers.16,17 From our previous studies using the volume fraction of PEG, we understand that ionic conductivity results from the rearrangement of ether units. For this work, the Vf,PEG concept has been extended to include the ethers of PPG, making Vf,ether. In our heterocopolymers, both the MePEG and MePPG have repeating ether units, and can thus both participate in the overall ionic conductivity. Figure 3 shows a modified Forsythe
(0.0009), indicating that there is a strong relationship for these copolymers. Furthermore, when all of the MePEG/MePPG heterocopolymers were grouped together (i.e., both the MePEG7/MePPG2 copolymers and MePEG7/MePPG3 copolymers; open circles in Figure 1), the correlation again showed a much smaller slope, a poor R2 value (0.0505), and a high pvalue (0.6282). This indicates that the heterocopolymers with heteromonomers do not follow the Doolittle equation. There are two considerations to take into account. First, there is a clear mismatch of monomer sizes that may affect the viscosity, and second, there is also a great difference in the slopes (−2.26 and −0.329 for the MePPG homopolymers and MePEG7/MePPGx heterocopolymers) which, as mentioned above, is the material specific constant q in eq 7a. This result agrees with our previous results,20 where the Doolittle fit for heterogeneous copolymers showed only a moderate R2 value (0.5340), a low p-value (0.0020), and a shallow slope (−0.611). Those results indicated that the FFV and viscosity were correlated, but the moderate R2 and shallow slope suggest the correlation is not strong, and the low p-value indicates a significant correlation. The p-value is likely to be larger if the slope is small, and much more likely to be small with a larger slope; that is, it is harder for the correlation to occur randomly if the slope is larger. If this were the case, then the p-value may not be indicative of a correlation and the FFV and viscosity may only be moderately correlated for that set of heterogeneous copolymers. These taken together indicate that the structures of the different copolymers are significantly different (as mentioned above in the GPC and end group analysis discussion). That is, differences in reactivity and associational forces make the MePPG/MePPG homocopolymers have a different structure from the MePEG/MePPG heteropolymers. Also, this difference in structure results in a significant difference in the transport properties of the MePEG/MePPG heterocopolymers. Ionic Conductivity. The ionic conductivities of the copolymers were measured to determine the relationship between ionic conductivity and FFV for these copolymers. Figure 2 shows a Forsythe plot correlating the molar equivalent ionic conductivity (Λ) with the inverse of FFV for all copolymers at 25 °C according to the Forsythe equation (eq
Figure 3. Forsythe plot with volume fraction of ether (Vf,ether) for all MePEG7/MePPGx copolymers with the best fit linear line shown. y = −13.1827x − 9.2248, R2 = 0.6146, p-value < 0.00001.
plot with molar equivalent conductivity (Λ) correlated with Vf,ether (instead of FFV) for all copolymers at 25 °C. The linear best fit shown has a much greater slope than the Forsythe correlation with FFV shown in Figure 2. In addition, the correlation in Figure 3 has a much greater R2 value (0.6146) and a small p-value (
